1. What is the Z-Test for Proportions?

The z-test for proportions is a statistical method used to determine whether the observed proportion in a sample differs significantly from a hypothesized population proportion. It's commonly used in hypothesis testing for categorical data.

2. How Does the Calculator Work?

The calculator uses the z-test formula for single proportion:

Where:

• \( p \) — Sample proportion (observed proportion)
• \( p_0 \) — Hypothesized population proportion
• \( n \) — Sample size

Explanation: The formula calculates how many standard deviations the observed proportion is from the hypothesized proportion.

3. Interpretation of Results

Details: The z-score indicates how extreme the sample proportion is relative to the hypothesized proportion. Typically:

• |z| > 1.96 suggests significance at α = 0.05 (two-tailed)
• |z| > 2.58 suggests significance at α = 0.01 (two-tailed)

4. Using the Calculator

Tips:

• Enter proportions as decimals between 0 and 1
• Sample size must be a positive integer
• Ensure np₀ and n(1-p₀) are both ≥ 10 for valid results

5. Frequently Asked Questions (FAQ)

Q1: When should I use a z-test for proportions?
A: Use when testing if a sample proportion differs from a known population proportion, with a sufficiently large sample size (typically n > 30).

Q2: What's the difference between z-test and t-test?
A: z-test is for proportions (categorical data) while t-test is for means (continuous data). z-test assumes normal approximation is valid.

Q3: What if my sample size is small?
A: For small samples (n < 30) or when np₀ < 10, consider using exact binomial tests instead.

Q4: How do I interpret a negative z-score?
A: A negative z-score means the sample proportion is less than the hypothesized proportion.

Q5: What are common applications of this test?
A: Used in quality control, survey analysis, A/B testing, and any scenario comparing observed vs expected proportions.